Advanced Calculus - Fundamentals of Mathematics

Advanced Calculus - Fundamentals of Mathematics

Vector calculus is an essential mathematical tool for performing mathematical analysis of physical and natural phenomena. It is employed in advanced applications in the field of engineering and ...
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Solutions for Chapters

Pp. 149-176 (28)

Carlos Polanco


This chapter provides the complete solution to all the exercises pointed out at the end of each chapter of this book. The solutions not only indicate the final result, but the respective procedures are exhibited. It is recommended in all cases that the reader review the solutions to all the exercises.


Bordered Hessian matrix, Cartesian coordinates, Critical points, Cross product, Cylindrical coordinates, Differential forms, Directional derivatives, Divergence, Double riemann integral, Exterior derivative, Exterior product, Gauss’ theorem, Geometric product, Graph of vector valued-function, Grassmann algebra, Green’s theorem, Hessian matrix, L’Hospital’s rule, Implicit function theorem, Improper integral in space, Improper integral on a plane, Inner product, Inverse function theorem, Jacobian determinant, Line integral of vector functions, Maps in ℝ, Maps in ℝ2, Maps in ℝ3, Partial derivatives, Stokes’ theorem, Surface integral of vector functions, Taylor’s theorem, Triple riemann integral.


Department of Mathematics Faculty of Sciences Universidad Nacional Autónoma de México México City México.